Nonlinear and multifractal approaches of the geomagnetic field

Details Nonlinear and multifractal approaches of the geomagnetic field Nonlinear and multifractal approaches of the geomagnetic field

Feb 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999pepi..110..157h&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 110, Issue 3-4, p. 157-190.

Physics

4

Scientific paper

Recent nonlinear dynamics techniques have been developed to analyse chaotic time series data. We first summarize the procedure which gives an appropriate reconstruction of the unknown dynamics from scalar measurements in a pseudophase space. It permits, firstly, the representation of the trajectories of the dynamical system-they define an attractor when the system is dissipative-by preserving its topological properties. We then present the invariant measures and ergodic quantities such as the multifractal spectrum and Lyapunov exponents which can be estimated on the reconstructed attractor. The multifractal analysis provides us with a characterization of the scaling energy of the process whereas the Lyapunov exponent gives another statistical measure of the stability of the dynamics. The estimation of these quantities was tested on synthetic data. The nonlinear and multifractal analyses were finally applied to the hourly mean values of the magnetic field recorded at the Eskdalemuir (ESK) observatory over 79 years (692,520 data measurements for each component). The estimations of a 5-dimensional pseudo-phase space and a positive Lyapunov exponent confirm the possibility of low-dimensional deterministic chaos in the magnetic field observations at ESK observatory. The correlation between the solar activity (the Wolf number), the unstable nature of the magnetic field, and the singularity spectrum points out the forcing of the solar cycles on the dynamics of the magnetic field at ESK observatory.

Affiliated with

Also associated with

No associations

Rating

Nonlinear and multifractal approaches of the geomagnetic field does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nonlinear and multifractal approaches of the geomagnetic field, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlinear and multifractal approaches of the geomagnetic field will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-949092